Primordial Nucleosynthesis with a Decaying Tau Neutrino

A comprehensive study of the effect of an unstable tau neutrino on primordial nucleosynthesis is presented. The standard code for nucleosynthesis is modified to allow for a massive decaying tau neutrino whose daughter products include neutrinos, photons, $e^\pm$ pairs, and/or noninteracting (sterile) daughter products. Tau-neutrino decays influence primordial nucleosynthesis in three distinct ways: (i) the energy density of the decaying tau neutrino and its daughter products affect the expansion rate tending to increase $^4$He, D, and $^3$He production; (ii) electromagnetic (EM) decay products heat the EM plasma and dilute the baryon-to-photon ratio tending to decrease $^4$He production and increase D and $^3$He production; and (iii) electron neutrinos and antineutrinos produced by tau-neutrino decays increase the weak rates that govern the neutron-to-proton ratio, leading to decreased $^4$He production for short lifetimes ($\la 30\sec$) and masses less than about $10\MeV$ and increased $^4$He production for long lifetimes or large masses. The precise effect of a decaying tau neutrino on the yields of primordial nucleosynthesis and the mass-lifetime limits that follow depend crucially upon decay mode. We identify four generic decay modes that serve to bracket the wider range of possibilities: